A classification of rational languages by semilattice-ordered
monoids

Libor Polak

Abstract.
We prove here an Eilenberg type theorem: the so-called
conjunctive varieties of rational languages correspond to the
pseudovarieties of finite semilattice-ordered monoids.
Taking complements of members of a conjunctive variety of languages
we get a so-called disjunctive variety. We present here a non-trivial
example of such a variety together with an equational characterization of the
corresponding pseudovariety.